And second, the transport coefficients – the shear and bulk viscosities – remain constants, and we have recovered their values as in before (see, e.g., [1]}, [2]}, [3]}). That in particular means the famous \(\eta /s\)  ratio, computed for the most black holes and black branes of String Theory in AdS spacetimes to be \(\eta /s \le \hbar /4\pi k_B\)  [4]}, holds in the case: no violation of the KSS bound [5]} occurs. (Recall, the issue of violation of this bound was under the focus since establishing this result (see, e.g., [6]}, [7]}, [8]}, [9]}, [10]} for details).)
Nevertheless, the presence of a negative bulk viscosity still becomes a problem since, as it has been noted even in the early works on the Membrane Paradigm (cf. [2]}), it requires non-causal teleological boundary conditions (see [12]} for a review) that means the horizon fluid is anti-causal in a response [13]}. It does not concern isolated and dynamical horizons [14]}, [15]}, where the response is causal, hence the bulk viscosity is positive. However, dynamical horizons exist rather for time-dependent solutions than for static/stationary ones. Time-dependent extensions of the Kerr solution developed and studied in [16]}, [17]} look perspective to this end.
